draft-ietf-ippm-multimetrics-11.txt		draft-ietf-ippm-multimetrics-12.txt
	Network Working Group E. Stephan		Network Working Group E. Stephan
	Internet-Draft France Telecom		Internet-Draft France Telecom
	Intended status: Standards Track L. Liang		Intended status: Standards Track L. Liang
	Expires: October 30, 2009 University of Surrey		Expires: March 5, 2010 University of Surrey
	A. Morton		A. Morton
	AT&T Labs		AT&T Labs
	April 28, 2009		September 1, 2009
	IP Performance Metrics (IPPM) for spatial and multicast		IP Performance Metrics (IPPM) for spatial and multicast
	draft-ietf-ippm-multimetrics-11		draft-ietf-ippm-multimetrics-12
	Status of this Memo		Status of this Memo
	This Internet-Draft is submitted to IETF in full conformance with the		This Internet-Draft is submitted to IETF in full conformance with the
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	Trust the right to allow modifications of such material outside the		Trust the right to allow modifications of such material outside the
	IETF Standards Process. Without obtaining an adequate license from		IETF Standards Process. Without obtaining an adequate license from
	skipping to change at page 1, line 45		skipping to change at page 1, line 45
	and may be updated, replaced, or obsoleted by other documents at any		and may be updated, replaced, or obsoleted by other documents at any
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	This Internet-Draft will expire on October 30, 2009.		This Internet-Draft will expire on March 5, 2010.
	Copyright Notice		Copyright Notice
	Copyright (c) 2009 IETF Trust and the persons identified as the		Copyright (c) 2009 IETF Trust and the persons identified as the
	document authors. All rights reserved.		document authors. All rights reserved.
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	Provisions Relating to IETF Documents in effect on the date of		Provisions Relating to IETF Documents in effect on the date of
	publication of this document (http://trustee.ietf.org/license-info).		publication of this document (http://trustee.ietf.org/license-info).
	Please review these documents carefully, as they describe your rights		Please review these documents carefully, as they describe your rights
	skipping to change at page 3, line 14		skipping to change at page 3, line 14
	Table of Contents		Table of Contents
	1. Introduction and Scope . . . . . . . . . . . . . . . . . . . . 4		1. Introduction and Scope . . . . . . . . . . . . . . . . . . . . 4
	2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4		2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
	3. Brief Metric Descriptions . . . . . . . . . . . . . . . . . . 8		3. Brief Metric Descriptions . . . . . . . . . . . . . . . . . . 8
	4. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . 10		4. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . 10
	5. Spatial vector metrics definitions . . . . . . . . . . . . . . 12		5. Spatial vector metrics definitions . . . . . . . . . . . . . . 12
	6. Spatial Segment Metrics Definitions . . . . . . . . . . . . . 19		6. Spatial Segment Metrics Definitions . . . . . . . . . . . . . 19
	7. One-to-group metrics definitions . . . . . . . . . . . . . . . 24		7. One-to-group metrics definitions . . . . . . . . . . . . . . . 24
	8. One-to-group Sample Statistics . . . . . . . . . . . . . . . . 27		8. One-to-group Sample Statistics . . . . . . . . . . . . . . . . 28
	9. Measurement Methods: Scalability and Reporting . . . . . . . . 37		9. Measurement Methods: Scalability and Reporting . . . . . . . . 37
	10. Manageability Considerations . . . . . . . . . . . . . . . . . 40		10. Manageability Considerations . . . . . . . . . . . . . . . . . 41
	11. Security Considerations . . . . . . . . . . . . . . . . . . . 45		11. Security Considerations . . . . . . . . . . . . . . . . . . . 45
	12. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 46		12. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 47
	13. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 46		13. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 47
	14. References . . . . . . . . . . . . . . . . . . . . . . . . . . 50		14. References . . . . . . . . . . . . . . . . . . . . . . . . . . 51
	14.1. Normative References . . . . . . . . . . . . . . . . . . 50		14.1. Normative References . . . . . . . . . . . . . . . . . . 51
	14.2. Informative References . . . . . . . . . . . . . . . . . 51		14.2. Informative References . . . . . . . . . . . . . . . . . 52
	Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 51		Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 52
	1. Introduction and Scope		1. Introduction and Scope
	IETF has standardized IP Performance Metrics (IPPM) for measuring		IETF has standardized IP Performance Metrics (IPPM) for measuring
	end-to-end performance between two points. This memo defines two new		end-to-end performance between two points. This memo defines two new
	categories of metrics that extend the coverage to multiple		categories of metrics that extend the coverage to multiple
	measurement points. It defines spatial metrics for measuring the		measurement points. It defines spatial metrics for measuring the
	performance of segments of a source to destination path, and metrics		performance of segments of a source to destination path, and metrics
	for measuring the performance between a source and many destinations		for measuring the performance between a source and many destinations
	in multiparty communications (e.g., a multicast tree).		in multiparty communications (e.g., a multicast tree).
	skipping to change at page 5, line 9		skipping to change at page 5, line 9
	2.1. Naming of the metrics		2.1. Naming of the metrics
	The names of the metrics, including capitalization letters, are as		The names of the metrics, including capitalization letters, are as
	close as possible of the names of the one-way end-to-end metrics they		close as possible of the names of the one-way end-to-end metrics they
	are derived from.		are derived from.
	2.2. Terms Defined Elsewhere		2.2. Terms Defined Elsewhere
	host: section 5 of RFC 2330		host: section 5 of RFC 2330
			router: section 5 of RFC 2330
	loss threshold: section 2.8.2 of RFC 2680		loss threshold: section 2.8.2 of RFC 2680
	path: section 5 of RFC 2330		path: section 5 of RFC 2330
	path digest: section 5 of RFC 2330
	sample: section 11 of RFC 2330		sample: section 11 of RFC 2330
	singleton: section 11 of RFC 2330		singleton: section 11 of RFC 2330
	2.3. Path Digest Hosts		2.3. Routers Digest
	The list of the hosts on a path from the source to the destination,		The list of the routers on the path from the source to the
	also referred to as the host path digest.		destination which act as points of interest, also referred to as the
			routers digest.
	2.4. Multiparty metric		2.4. Multiparty metric
	A metric is said to be multiparty if the topology involves more than		A metric is said to be multiparty if the topology involves more than
	one measurement collection point. All multiparty metrics designate a		one measurement collection point. All multiparty metrics designate a
	set of hosts as "points of interest", where one host is the source		set of hosts as "points of interest", where one host is the source
	and other hosts are the measurement collection points. For example,		and other hosts are the measurement collection points. For example,
	if the set of points of interest is < ha, hb, hc, ..., hn >, where ha		if the set of points of interest is < ha, hb, hc, ..., hn >, where ha
	is the source and < hb, hc, ..., hn > are the destinations, then		is the source and < hb, hc, ..., hn > are the destinations, then
	measurements may be conducted between < ha, hb>, < ha, hc>, ..., <ha,		measurements may be conducted between < ha, hb>, < ha, hc>, ..., <ha,
	hn >.		hn >.
	For the purposes of this memo (reflecting the scope of a single		For the purposes of this memo (reflecting the scope of a single
	source), the only multiparty metrics are one-to-group metrics.		source), the only multiparty metrics are one-to-group metrics.
	2.5. Spatial metric		2.5. Spatial metric
	A metric is said to be spatial if one of the hosts (measurement		A metric is said to be spatial if one of the hosts (measurement
	collection points) involved is neither the source nor a destination		collection points) involved is neither the source nor a destination
	of the measured packet(s). Such measurement hosts will usually be		of the measured packet(s). Such measurement hosts will usually be
	members of the path digest.		routers member of the routers digest.
	2.6. One-to-group metric		2.6. One-to-group metric
	A metric is said to be one-to-group if the measured packet is sent by		A metric is said to be one-to-group if the measured packet is sent by
	one source and (potentially) received by more than one destination.		one source and (potentially) received by more than one destination.
	Thus, the topology of the communication group can be viewed as a		Thus, the topology of the communication group can be viewed as a
	center-distributed or server-client topology with the source as the		center-distributed or server-client topology with the source as the
	center/server in the topology.		center/server in the topology.
	2.7. Points of interest		2.7. Points of interest
	Points of interest are the hosts (as per the RFC 2330 definition,		Points of interest are the hosts (as per the RFC 2330 definition,
	"hosts" include routing nodes) that are measurement collection		"hosts" include routing nodes) that are measurement collection
	points, a sub-set of the set of hosts involved in the delivery of the		points, a sub-set of the set of hosts involved in the delivery of the
	packets (in addition to the source itself).		packets (in addition to the source itself).
	For spatial metrics, points of interest are a (possibly arbitrary)		For spatial metrics, points of interest are a (possibly arbitrary)
	sub-set of all the hosts involved in the path.		sub-set of all the routers involved in the path.
	Points of interest of one-to-group metrics are the intended		Points of interest of one-to-group metrics are the intended
	destination hosts for packets from the source (in addition to the		destination hosts for packets from the source (in addition to the
	source itself).		source itself).
	Src Dst		Src Dst
	`. ,-.		`. ,-.
	`. ,' `...... 1		`. ,' `...... 1
	`. ; :		`. ; :
	`. ; :		`. ; :
	; :... 2		; :... 2
	| |		| |
	: ;		: ;
	: ;.... 3		: ;.... 3
	: ;		: ;
	`. ,'		`. ,'
	`-'....... I		`-'....... I
	Figure 1: One-to-group points of interest		Figure 1: One-to-group points of interest
	A candidate point of interest for spatial metrics is a host from the		A candidate point of interest for spatial metrics is a router from
	set of hosts involved in the delivery of the packets from source to		the set of routers involved in the delivery of the packets from
	destination.		source to destination.
	Src ------. Hosts		Src ------. Hosts
	\		\
	`---X ... 1		`---X --- 1
	\		\
	x		x
	/		/
	.---------X .... 2		.---------X ---- 2
	/		/
	x		x
	\		...
	`---X .... 3		`---X ---- ...
	\		\
	\		\
	\		\
	X .... J		X ---- J
	\		\
	\		\
	\		\
	`---- Dst		`---- Dst
	Note: 'x' are nodes which are not points of interest		Note: 'X' are nodes which are points of interest,
			'x' are nodes which are not points of interest
	Figure 2: Spatial points of interest		Figure 2: Spatial points of interest
	2.8. Reference point		2.8. Reference point
	A reference point is defined as the server where the statistical		A reference point is defined as the server where the statistical
	calculations will be carried out. It is usually a centralized server		calculations will be carried out. It is usually a centralized server
	in the measurement architecture that is controlled by a network		in the measurement architecture that is controlled by a network
	operator, where measurement data can be collected for further		operator, where measurement data can be collected for further
	processing. The reference point is distinctly different from hosts		processing. The reference point is distinctly different from hosts
	skipping to change at page 8, line 48		skipping to change at page 8, line 50
	vector matrix		vector matrix
	(space) (time and space)		(space) (time and space)
	Figure 3: Relationship between singletons, samples, vectors and		Figure 3: Relationship between singletons, samples, vectors and
	matrix		matrix
	3. Brief Metric Descriptions		3. Brief Metric Descriptions
	The metrics for spatial and one-to-group measurement are based on the		The metrics for spatial and one-to-group measurement are based on the
	source-to-destination, or end-to-end metrics defined by IETF in		source-to-destination, or end-to-end metrics defined by IETF in
	[[RFC2679], [RFC2680], [RFC3393], [RFC3432].		[RFC2679], [RFC2680], [RFC3393], [RFC3432].
	This memo defines seven new spatial metrics using the [RFC2330]		This memo defines seven new spatial metrics using the [RFC2330]
	framework of parameters, units of measure, and measurement		framework of parameters, units of measure, and measurement
	methodologies. Each definition includes a section that describes		methodologies. Each definition includes a section that describes
	measurements constraints and issues, and provides guidance to		measurements constraints and issues, and provides guidance to
	increase the accuracy of the results.		increase the accuracy of the results.
	The spatial metrics are:		The spatial metrics are:
	o Type-P-Spatial-One-way-Delay-Vector divides the end-to-end Type-P-		o Type-P-Spatial-One-way-Delay-Vector divides the end-to-end Type-P-
	One-way-Delay [RFC2679] into a spatial vector of one-way delay		One-way-Delay [RFC2679] into a spatial vector of one-way delay
	singletons.		singletons.
	o Type-P-Spatial-One-way-Packet-Loss-Vector divides an end-to-end		o Type-P-Spatial-One-way-Packet-Loss-Vector divides an end-to-end
	Type-P-One-way-Packet-Loss [RFC2680] into a spatial vector of		Type-P-One-way-Packet-Loss [RFC2680] into a spatial vector of
	packet loss singletons.		packet loss singletons.
	o Type-P-Spatial-One-way-ipdv-Vector divides an end-to-end Type-P-		o Type-P-Spatial-One-way-ipdv-Vector divides an end-to-end Type-P-
	One-way-ipdv into a spatial vector of ipdv singletons.		One-way-ipdv into a spatial vector of ipdv (IP Packet Delay
			Variation) singletons.
	o Using elements of the Type-P-Spatial-One-way-Delay-Vector metric,		o Using elements of the Type-P-Spatial-One-way-Delay-Vector metric,
	a sample called Type-P-Segment-One-way-Delay-Stream collects one-		a sample called Type-P-Segment-One-way-Delay-Stream collects one-
	way delay metrics between two points of interest on the path over		way delay metrics between two points of interest on the path over
	time.		time.
	o Likewise, using elements of the Type-P-Spatial-Packet-Loss-Vector		o Likewise, using elements of the Type-P-Spatial-Packet-Loss-Vector
	metric, a sample called Type-P-Segment-Packet-Loss-Stream collects		metric, a sample called Type-P-Segment-Packet-Loss-Stream collects
	one-way delay metrics between two points of interest on the path		one-way delay metrics between two points of interest on the path
	over time.		over time.
	o Using the Type-P-Spatial-One-way-Delay-Vector metric, a sample		o Using the Type-P-Spatial-One-way-Delay-Vector metric, a sample
	called Type-P-Segment-ipdv-prev-Stream, will be introduced to		called Type-P-Segment-ipdv-prev-Stream, will be introduced to
	skipping to change at page 10, line 46		skipping to change at page 11, line 4
	metrics and one to multipoint metrics.		metrics and one to multipoint metrics.
	4.1. Motivations for spatial metrics		4.1. Motivations for spatial metrics
	Spatial metrics are needed for:		Spatial metrics are needed for:
	o Decomposing the performance of an inter-domain path to quantify		o Decomposing the performance of an inter-domain path to quantify
	the per-AS contribution to the end-to-end performance.		the per-AS contribution to the end-to-end performance.
	o Traffic engineering and troubleshooting, which benefit from		o Traffic engineering and troubleshooting, which benefit from
	spatial views of one-way delay and ipdv consumption, or		spatial views of one-way delay and ipdv consumption, or
	identification of the path segment where packets were lost.		identification of the path segment where packets were lost.
	o Monitoring the decomposed performance of a multicast tree based on		o Monitoring the decomposed performance of a multicast tree based on
	of MPLS point-to-multipoint communications.		MPLS point-to-multipoint communications.
	o Dividing end-to-end metrics, so that some segment measurements can		o Dividing end-to-end metrics, so that some segment measurements can
	be re-used and help measurement systems reach large-scale		be re-used and help measurement systems reach large-scale
	coverage. Spatial measures could characterize the performance of		coverage. Spatial measures could characterize the performance of
	an intra-domain segment and provide an elementary piece of		an intra-domain segment and provide an elementary piece of
	information needed to estimate inter-domain performance to another		information needed to estimate inter-domain performance to another
	destination using Spatial Composition metrics		destination using Spatial Composition metrics
	[I-D.ietf-ippm-spatial-composition].		[I-D.ietf-ippm-spatial-composition].
	4.2. Motivations for One-to-group metrics		4.2. Motivations for One-to-group metrics
	skipping to change at page 13, line 19		skipping to change at page 13, line 19
	related to methodology, clock, uncertainties and reporting.		related to methodology, clock, uncertainties and reporting.
	5.1.1. Metric Name		5.1.1. Metric Name
	Type-P-Spatial-One-way-Delay-Vector		Type-P-Spatial-One-way-Delay-Vector
	5.1.2. Metric Parameters		5.1.2. Metric Parameters
	o Src*, the IP address of the sender.		o Src*, the IP address of the sender.
	o Dst*, the IP address of the receiver.		o Dst*, the IP address of the receiver.
	o i, an integer in the ordered list <1,2,...,n> of hosts in the		o i, an integer in the ordered list <1,2,...,n> of routers in the
	path.		path.
	o Hi, a host in the path digest.		o Hi, a router of the routers digest.
	o T*, a time, the sending (or initial observation) time for a		o T*, a time, the sending (or initial observation) time for a
	measured packet.		measured packet.
	o dT*, a delay, the one-way delay for a measured packet.		o dT*, a delay, the one-way delay for a measured packet.
	o dTi, a delay, the one-way delay for a measured packet from the		o dTi, a delay, the one-way delay for a measured packet from the
	source to host Hi.		source to router Hi.
	o <dT1,... dTi,... dTn> a list of n delay singletons.		o <dT1,... dTi,... dTn> a list of n delay singletons.
	o Type-P*, the specification of the packet type.		o Type-P*, the specification of the packet type.
	o <H1, H2,..., Hn>, a path host digest.		o <H1, H2,..., Hn> the routers digest.
	5.1.3. Metric Units		5.1.3. Metric Units
	The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of		The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of
	times (a real number in the dimension of seconds with sufficient		times (a real number in the dimension of seconds with sufficient
	resolution to convey the results).		resolution to convey the results).
	5.1.4. Definition		5.1.4. Definition
	Given a Type-P packet sent by the Src at wire-time (first bit) T to		Given a Type-P packet sent by the Src at wire-time (first bit) T to
	skipping to change at page 14, line 8		skipping to change at page 14, line 8
	(last bit received) Hi, or undefined if the packet does not pass Hi		(last bit received) Hi, or undefined if the packet does not pass Hi
	within a specified loss threshold* time.		within a specified loss threshold* time.
	Type-P-Spatial-One-way-Delay-Vector metric is defined for the path		Type-P-Spatial-One-way-Delay-Vector metric is defined for the path
	<Src, H1, H2,..., Hn, Dst> as the sequence of values		<Src, H1, H2,..., Hn, Dst> as the sequence of values
	<T,dT1,dT2,...,dTn,dT>.		<T,dT1,dT2,...,dTn,dT>.
	5.1.5. Discussion		5.1.5. Discussion
	Some specific issues that may occur are as follows:		Some specific issues that may occur are as follows:
	o the delay singletons "appear" to decrease: dTi > DTi+1. This may		o the delay singletons "appear" to decrease: dTi > dTi+1. This may
	occur despite being physically impossible with the definition		occur despite being physically impossible with the definition
	used.		used.
	* This is frequently due to a measurement clock synchronization		* This is frequently due to a measurement clock synchronization
	issue. This point is discussed in the section 3.7.1. "Errors		issue. This point is discussed in the section 3.7.1. "Errors
	or uncertainties related to Clocks" of [RFC2679].		or uncertainties related to Clocks" of [RFC2679].
	Consequently, the values of delays measured at multiple hosts		Consequently, the values of delays measured at multiple routers
	may not match the order of those hosts on the path.		may not match the order of those routers on the path.
	* The actual order of hosts on the path may change due to		* The actual order of routers on the path may change due to
	reconvergence (e.g., recovery from a link failure).		reconvergence (e.g., recovery from a link failure).
	* The location of the measurement collection point in the device		* The location of the measurement collection point in the device
	influences the result. If the packet is not observed directly		influences the result. If the packet is not observed directly
	on the input interface the delay includes buffering time and		on the input interface the delay includes buffering time and
	consequently an uncertainty due to the difference between 'wire		consequently an uncertainty due to the difference between 'wire
	time' and 'host time'.		time' and 'host time'.
	5.2. A Definition for Spatial Packet Loss Vector		5.2. A Definition for Spatial Packet Loss Vector
	This section is coupled with the definition of Type-P-One-way-Packet-		This section is coupled with the definition of Type-P-One-way-Packet-
	Loss. When a parameter from the section 2 of [RFC2680] is used in		Loss. When a parameter from section 2 of [RFC2680] is used in this
	this section, the first instance will be tagged with a trailing		section, the first instance will be tagged with a trailing asterisk.
	asterisk.
	Sections 2.5 to 2.8 of [RFC2680] give requirements and applicability		Sections 2.5 to 2.8 of [RFC2680] give requirements and applicability
	statements for end-to-end one-way packet loss measurements. They are		statements for end-to-end one-way packet loss measurements. They are
	applicable to each point of interest, Hi, involved in the measure.		applicable to each point of interest, Hi, involved in the measure.
	Spatial packet loss measurement MUST respect them, especially those		Spatial packet loss measurement MUST respect them, especially those
	related to methodology, clock, uncertainties and reporting.		related to methodology, clock, uncertainties and reporting.
	The following sections define the spatial loss vector, adapt some of		The following sections define the spatial loss vector, adapt some of
	the points above, and introduce points specific to spatial loss		the points above, and introduce points specific to spatial loss
	measurement.		measurement.
	5.2.1. Metric Name		5.2.1. Metric Name
	Type-P-Spatial-Packet-Loss-Vector		Type-P-Spatial-Packet-Loss-Vector
	5.2.2. Metric Parameters		5.2.2. Metric Parameters
	o Src*, the IP address of the sender.		o Src*, the IP address of the sender.
	o Dst*, the IP address of the receiver.		o Dst*, the IP address of the receiver.
	o i, an integer in the ordered list <1,2,...,n> of hosts in the		o i, an integer in the ordered list <1,2,...,n> of routers in the
	path.		path.
			o Hi, a router of the routers digest.
	o Hi, points of interest from the path digest.
	o T*, a time, the sending time for a measured packet.		o T*, a time, the sending time for a measured packet.
	o dTi, a delay, the one-way delay for a measured packet from the		o dTi, a delay, the one-way delay for a measured packet from the
	source to host Hi.		source to host Hi.
	o <dT1,..., dTn>, list of n delay singletons.		o <dT1,..., dTn>, list of n delay singletons.
	o Type-P*, the specification of packet type.		o Type-P*, the specification of packet type.
	o <H1, H2,..., Hn>, a host path digest.		o <H1, H2,..., Hn>, the routers digest.
	o <L1, L2, ...,Ln>, a list of Boolean values.		o <L1, L2, ...,Ln>, a list of Boolean values.
	5.2.3. Metric Units		5.2.3. Metric Units
	The value of Type-P-Spatial-Packet-Loss-Vector is a sequence of		The value of Type-P-Spatial-Packet-Loss-Vector is a sequence of
	Boolean values.		Boolean values.
	5.2.4. Definition		5.2.4. Definition
	Given a Type-P packet sent by the Src at time T to the receiver Dst		Given a Type-P packet sent by the Src at time T to the receiver Dst
	skipping to change at page 15, line 35		skipping to change at page 15, line 34
	of values <T, L1, L2, ..., Ln> such that for each Hi of the path, a		of values <T, L1, L2, ..., Ln> such that for each Hi of the path, a
	value of 0 for Li means that dTi is a finite value, and a value of 1		value of 0 for Li means that dTi is a finite value, and a value of 1
	means that dTi is undefined.		means that dTi is undefined.
	5.2.5. Discussion		5.2.5. Discussion
	Some specific issues that may occur are as follows:		Some specific issues that may occur are as follows:
	o The result might include the sequence of values 1,0. Although		o The result might include the sequence of values 1,0. Although
	this appears physically impossible (a packet is lost, then re-		this appears physically impossible (a packet is lost, then re-
	appears later on the path):		appears later on the path):
	* The actual hosts on the path may change due to reconvergence		* The actual routers on the path may change due to reconvergence
	(e.g., recovery from a link failure).		(e.g., recovery from a link failure).
	* The order of hosts on the path may change due to reconvergence.		* The order of routers on the path may change due to
	* A packet may not be observed in a host due to some buffer or		reconvergence.
			* A packet may not be observed in a router due to some buffer or
	CPU overflow at the measurement collection point.		CPU overflow at the measurement collection point.
	5.3. A Definition for Spatial One-way Ipdv Vector		5.3. A Definition for Spatial One-way Ipdv Vector
	When a parameter from section 2 of [RFC3393] (the definition of Type-		When a parameter from section 2 of [RFC3393] (the definition of Type-
	P-One-way-ipdv) is used in this section, the first instance will be		P-One-way-ipdv) is used in this section, the first instance will be
	tagged with a trailing asterisk.		tagged with a trailing asterisk.
	The following sections define the spatial ipdv vector, adapt some of		The following sections define the spatial ipdv vector, adapt some of
	the points above, and introduce points specific to spatial ipdv		the points above, and introduce points specific to spatial ipdv
	measurement.		measurement.
	5.3.1. Metric Name		5.3.1. Metric Name
	Type-P-Spatial-One-way-ipdv-Vector		Type-P-Spatial-One-way-ipdv-Vector
	5.3.2. Metric Parameters		5.3.2. Metric Parameters
	o Src*, the IP address of the sender.		o Src*, the IP address of the sender.
	o Dst*, the IP address of the receiver.		o Dst*, the IP address of the receiver.
	o i, an integer in the ordered list <1,2,...,n> of hosts in the		o i, an integer in the ordered list <1,2,...,n> of routers in the
	path.		path.
	o Hi, a host of the path digest.		o Hi, a router of the routers digest.
	o T1*, a time, the sending time for a first measured packet.		o T1*, a time, the sending time for a first measured packet.
	o T2*, a time, the sending time for a second measured packet.		o T2*, a time, the sending time for a second measured packet.
	o dT*, a delay, the one-way delay for a measured packet.		o dT*, a delay, the one-way delay for a measured packet.
	o dTi, a delay, the one-way delay for a measured packet from the		o dTi, a delay, the one-way delay for a measured packet from the
	source to host Hi.		source to router Hi.
	o Type-P*, the specification of the packets type.		o Type-P*, the specification of the packets type.
	o P1, the first packet sent at time T1.		o P1, the first packet sent at time T1.
	o P2, the second packet sent at time T2.		o P2, the second packet sent at time T2.
	o <H1, H2,..., Hn>, a host path digest.		o <H1, H2,..., Hn>, the routers digest.
	o <T1,dT1.1, dT1.2,..., dT1.n,dT1>, the Type-P-Spatial-One-way-		o <T1,dT1.1, dT1.2,..., dT1.n,dT1>, the Type-P-Spatial-One-way-
	Delay-Vector for packet sent at time T1.		Delay-Vector for packet sent at time T1.
	o <T2,dT2.1, dT2.2,..., dT2.n,dT2>, the Type-P-Spatial-One-way-		o <T2,dT2.1, dT2.2,..., dT2.n,dT2>, the Type-P-Spatial-One-way-
	Delay-Vector for packet sent at time T2.		Delay-Vector for packet sent at time T2.
	o L*, a packet length in bits. The packets of a Type P packet		o L*, a packet length in bits. The packets of a Type P packet
	stream from which the Type-P-Spatial-One-way-Delay-Vector metric		stream from which the Type-P-Spatial-One-way-Delay-Vector metric
	is taken MUST all be of the same length.		is taken MUST all be of the same length.
	5.3.3. Metric Units		5.3.3. Metric Units
	The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of		The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of
	times (a real number in the dimension of seconds with sufficient		times (a real number in the dimension of seconds with sufficient
	resolution to convey the results).		resolution to convey the results).
	5.3.4. Definition		5.3.4. Definition
	Given P1 the Type-P packet sent by the sender Src at wire-time (first		Given P1 the Type-P packet sent by the sender Src at wire-time (first
	bit) T1 to the receiver Dst and <T1, dT1.1, dT1.2,..., dT1.n, dT1>		bit) T1 to the receiver Dst and <T1, dT1.1, dT1.2,..., dT1.n, dT1>
	its Type-P-Spatial-One-way-Delay-Vector over the path <H1, H2,...,		its Type-P-Spatial-One-way-Delay-Vector over the sequence of routers
	Hn>.		<H1, H2,..., Hn>.
	Given P2 the Type-P packet sent by the sender Src at wire-time (first		Given P2 the Type-P packet sent by the sender Src at wire-time (first
	bit) T2 to the receiver Dst and <T2, dT2.1, dT2.2,..., dT2.n, dT2>		bit) T2 to the receiver Dst and <T2, dT2.1, dT2.2,..., dT2.n, dT2>
	its Type-P-Spatial-One-way-Delay-Vector over the same path.		its Type-P-Spatial-One-way-Delay-Vector over the same path.
	Type-P-Spatial-One-way-ipdv-Vector metric is defined as the sequence		Type-P-Spatial-One-way-ipdv-Vector metric is defined as the sequence
	of values <T1, T2, dT2.1-dT1.1, dT2.2-dT1.2 ,..., dT2.n-dT1.n, dT2-		of values <T1, T2, dT2.1-dT1.1, dT2.2-dT1.2 ,..., dT2.n-dT1.n, dT2-
	dT1> such that for each Hi of the path <H1, H2,..., Hn>, dT2.i-dT1.i		dT1> such that for each Hi of the sequence of routers <H1, H2,...,
	is either a real number if the packets P1 and P2 pass Hi at wire-time		Hn>, dT2.i-dT1.i is either a real number if the packets P1 and P2
	(last bit) dT1.i and dT2.i respectively, or undefined if at least one		pass Hi at wire-time (last bit) dT1.i and dT2.i respectively, or
	of them never passes Hi (and the respective one-way delay is		undefined if at least one of them never passes Hi (and the respective
	undefined). The T1,T2* pair indicates the inter-packet emission		one-way delay is undefined). The T1,T2* pair indicates the inter-
	interval and dT2-dT1 is ddT* the Type-P-One-way-ipdv.		packet emission interval and dT2-dT1 is ddT* the Type-P-One-way-ipdv.
	5.4. Spatial Methodology		5.4. Spatial Methodology
	The methodology, reporting specifications, and uncertainties		The methodology, reporting specifications, and uncertainties
	specified in section 3 of [RFC2679] apply to each point of interest		specified in section 3 of [RFC2679] apply to each point of interest
	(or measurement collection point), Hi, measuring an element of a		(or measurement collection point), Hi, measuring an element of a
	spatial delay vector.		spatial delay vector.
	Likewise, the methodology, reporting specifications, and		Likewise, the methodology, reporting specifications, and
	uncertainties specified in section 2 of [RFC2680] apply to each point		uncertainties specified in section 2 of [RFC2680] apply to each point
	skipping to change at page 18, line 32		skipping to change at page 18, line 32
	may be computed as infinite by one observation point but as a real		may be computed as infinite by one observation point but as a real
	value by another one, or may be measured as a real value by the last		value by another one, or may be measured as a real value by the last
	observation point of the path but designated as undefined by Dst.		observation point of the path but designated as undefined by Dst.
	The observation/measurement collection points and the destination		The observation/measurement collection points and the destination
	SHOULD use consistent methods to detect packets losses. The methods		SHOULD use consistent methods to detect packets losses. The methods
	and parameters must be systematically reported to permit careful		and parameters must be systematically reported to permit careful
	comparison and to avoid introducing any confounding factors in the		comparison and to avoid introducing any confounding factors in the
	analysis.		analysis.
	5.4.2. Host Path Digest		5.4.2. Routers Digest
	The methodology given above relies on knowing the order of the hosts/		The methodology given above relies on knowing the order of the
	measurement collection points on the path [RFC2330].		router/measurement collection points on the path [RFC2330].
	Path instability might cause a test packet to be observed more than		Path instability might cause a test packet to be observed more than
	once by the same host, resulting in the repetition of one or more		once by the same router, resulting in the repetition of one or more
	hosts in the Path Digest.		routers in the routers digest.
	For example, repeated observations may occur during rerouting phases		For example, repeated observations may occur during rerouting phases
	which introduce temporary micro loops. During such an event the host		which introduce temporary micro loops. During such an event the
	path digest for a packet crossing Ha and Hb may include the pattern		routers digest for a packet crossing Ha and Hb may include the
	<Hb, Ha, Hb, Ha, Hb> meaning that Ha ended the computation of the new		pattern <Hb, Ha, Hb, Ha, Hb> meaning that Ha ended the computation of
	path before Hb and that the initial path was from Ha to Hb and that		the new path before Hb and that the initial path was from Ha to Hb
	the new path is from Hb to Ha.		and that the new path is from Hb to Ha.
	Consequently, duplication of hosts in the path digest of a vector		Consequently, duplication of routers in the routers digest of a
	MUST be identified before computation of statistics to avoid		vector MUST be identified before computation of statistics to avoid
	producing corrupted information.		producing corrupted information.
	6. Spatial Segment Metrics Definitions		6. Spatial Segment Metrics Definitions
	This section defines samples to measure the performance of a segment		This section defines samples to measure the performance of a segment
	of a path over time. The definitions rely on the matrix of the		of a path over time. The definitions rely on the matrix of the
	spatial vector metrics defined above.		spatial vector metrics defined above.
	Firstly this section defines a sample of one-way delay, Type-P-		Firstly this section defines a sample of one-way delay, Type-P-
	Segment-One-way-Delay-Stream, and a sample of packet loss, Type-P-		Segment-One-way-Delay-Stream, and a sample of packet loss, Type-P-
	segment-Packet-Loss-Stream.		segment-Packet-Loss-Stream.
	Then it defines 2 different samples of ipdv: Type-P-Segment-ipdv-		Then it defines 2 different samples of ipdv: Type-P-Segment-ipdv-
	prev-Stream uses the current and previous packets as the selection		prev-Stream uses the current and previous packets as the selection
	function, and Type-P-Segment-ipdv-min-Stream, uses the minimum delay		function, and Type-P-Segment-ipdv-min-Stream, uses the minimum delay
	as one of the selected packets in every pair.		as one of the selected packets in every pair.
	6.1. A Definition of a Sample of One-way Delay of a Segment of the Path		6.1. A Definition of a Sample of One-way Delay of a Segment of the Path
	This metric defines a sample of One-way delays over time between a		This metric defines a sample of One-way delays over time between a
	pair of hosts on a path. Since it is very close semantically to the		pair of routers on a path. Since it is very close semantically to
	metric Type-P-One-way-Delay-Poisson-Stream defined in section 4 of		the metric Type-P-One-way-Delay-Poisson-Stream defined in section 4
	[RFC2679], sections 4.5 to 4.8 of [RFC2679] are integral parts of the		of [RFC2679], sections 4.5 to 4.8 of [RFC2679] are integral parts of
	definition text below.		the definition text below.
	6.1.1. Metric Name		6.1.1. Metric Name
	Type-P-Segment-One-way-Delay-Stream		Type-P-Segment-One-way-Delay-Stream
	6.1.2. Metric Parameters		6.1.2. Metric Parameters
	o Src, the IP address of the sender.		o Src, the IP address of the sender.
	o Dst, the IP address of the receiver.		o Dst, the IP address of the receiver.
	o Type-P, the specification of the packet type.		o Type-P, the specification of the packet type.
	o i, an integer in the ordered list <1,2,...,n> of hosts in the		o i, an integer in the ordered list <1,2,...,n> of routers in the
	path.		path.
	o k, an integer which orders the packets sent.		o k, an integer which orders the packets sent.
	o a and b, two integers where b > a.		o a and b, two integers where b > a.
	o Hi, a host of the path digest.		o Hi, a router of the routers digest.
	o <H1,..., Ha, ..., Hb, ...., Hn>, a host path digest.		o <H1,..., Ha, ..., Hb, ...., Hn>, the routers digest.
	o <T1, T2, ..., Tm>, a list of times.		o <T1, T2, ..., Tm>, a list of times.
	6.1.3. Metric Units		6.1.3. Metric Units
	The value of a Type-P-Segment-One-way-Delay-Stream is a pair of:		The value of a Type-P-Segment-One-way-Delay-Stream is a pair of:
	A list of times <T1, T2, ..., Tm>;		A list of times <T1, T2, ..., Tm>;
	A sequence of delays.		A sequence of delays.
	6.1.4. Definition		6.1.4. Definition
	Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb, ...,		Given two routers, Ha and Hb, of the the path <H1, H2,..., Ha, ...,
	Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for the		Hb, ..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector
	packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :		for the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm>
			:
	<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>;		<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>;
	<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>;		<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>;
	...		...
	<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.		<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.
	We define the sample Type-P-segment-One-way-Delay-Stream as the		We define the sample Type-P-segment-One-way-Delay-Stream as the
	sequence <dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab> such that for		sequence <dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab> such that for
	each time Tk, 'dTk.ab' is either the real number 'dTk.b - dTk.a' if		each time Tk, 'dTk.ab' is either the real number 'dTk.b - dTk.a' if
	the packet sent at time Tk passes Ha and Hb or undefined if this		the packet sent at time Tk passes Ha and Hb or undefined if this
	packet never passes Ha or (inclusive) never passes Hb.		packet never passes Ha or (inclusive) never passes Hb.
	skipping to change at page 20, line 39		skipping to change at page 20, line 40
	through optical fiber facilities is 2.5ms, but the measurement		through optical fiber facilities is 2.5ms, but the measurement
	collection point has a clock resolution of 8ms.		collection point has a clock resolution of 8ms.
	The metric SHALL be invalid for times < T1 , T2, ..., Tm-1, Tm> if		The metric SHALL be invalid for times < T1 , T2, ..., Tm-1, Tm> if
	the following conditions occur:		the following conditions occur:
	o Ha or Hb disappears from the path due to some routing change.		o Ha or Hb disappears from the path due to some routing change.
	o The order of Ha and Hb changes in the path.		o The order of Ha and Hb changes in the path.
	6.2. A Definition of a Sample of Packet Loss of a Segment of the Path		6.2. A Definition of a Sample of Packet Loss of a Segment of the Path
	This metric defines a sample of packet loss over time between a pair		This metric defines a sample of packet loss over time between a pair
	of hosts of a path. Since it is very close semantically to the		of routers of a path. Since it is very close semantically to the
	metric Type-P-Packet-loss-Stream defined in section 3 of [RFC2680],		metric Type-P-Packet-loss-Stream defined in section 3 of [RFC2680],
	sections 3.5 to 3.8 of [RFC2680] are integral parts of the definition		sections 3.5 to 3.8 of [RFC2680] are integral parts of the definition
	text below.		text below.
	6.2.1. Metric Name		6.2.1. Metric Name
	Type-P-segment-Packet-Loss-Stream		Type-P-segment-Packet-Loss-Stream
	6.2.2. Metric Parameters		6.2.2. Metric Parameters
	o Src, the IP address of the sender.		o Src, the IP address of the sender.
	o Dst, the IP address of the receiver.		o Dst, the IP address of the receiver.
	o Type-P, the specification of the packet type.		o Type-P, the specification of the packet type.
	o k, an integer which orders the packets sent.		o k, an integer which orders the packets sent.
	o n, an integer which orders the hosts on the path.		o n, an integer which orders the routers on the path.
	o a and b, two integers where b > a.		o a and b, two integers where b > a.
	o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, a host path digest.		o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers digest.
	o Hi, exchange points of the path digest.		o Hi, a router of the routers digest.
	o <T1, T2, ..., Tm>, a list of times.		o <T1, T2, ..., Tm>, a list of times.
	o <L1, L2, ..., Ln>, a list of Boolean values.		o <L1, L2, ..., Ln>, a list of Boolean values.
	6.2.3. Metric Units		6.2.3. Metric Units
	The value of a Type-P-segment-Packet-Loss-Stream is a pair of:		The value of a Type-P-segment-Packet-Loss-Stream is a pair of:
	A The list of times <T1, T2, ..., Tm>;		A The list of times <T1, T2, ..., Tm>;
	A sequence of Boolean values.		A sequence of Boolean values.
	6.2.4. Definition		6.2.4. Definition
	Given two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,		Given two routers, Ha and Hb, of the the path <H1, H2,..., Ha, ...,
	..., Hn>, and the matrix of Type-P-Spatial-Packet-Loss-Vector for the		Hb, ..., Hn>, and the matrix of Type-P-Spatial-Packet-Loss-Vector for
	packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :		the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :
	<T1, L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,		<T1, L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,
	<T2, L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L>,		<T2, L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L>,
	...,		...,
	<Tm, Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.		<Tm, Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.
	We define the value of the sample Type-P-segment-Packet-Lost-Stream		We define the value of the sample Type-P-segment-Packet-Loss-Stream
	from Ha to Hb as the sequence of Booleans <L1.ab, L2.ab,..., Lk.ab,		from Ha to Hb as the sequence of Booleans <L1.ab, L2.ab,..., Lk.ab,
	..., Lm.ab> such that for each Tk:		..., Lm.ab> such that for each Tk:
	o A value of Lk of 0 means that Ha and Hb observed the packet sent		o A value of Lk of 0 means that Ha and Hb observed the packet sent
	at time Tk (both Lk.a and Lk.b have a value of 0).		at time Tk (both Lk.a and Lk.b have a value of 0).
	o A value of Lk of 1 means that Ha observed the packet sent at time		o A value of Lk of 1 means that Ha observed the packet sent at time
	Tk (Lk.a has a value of 0) and that Hb did not observe the packet		Tk (Lk.a has a value of 0) and that Hb did not observe the packet
	sent at time Tk (Lk.b has a value of 1).		sent at time Tk (Lk.b has a value of 1).
	o The value of Lk is undefined when neither Ha nor Hb observed the		o The value of Lk is undefined when neither Ha nor Hb observed the
	packet (both Lk.a and Lk.b have a value of 1).		packet (both Lk.a and Lk.b have a value of 1).
	6.2.5. Discussion		6.2.5. Discussion
	Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-Loss-Stream		Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-Loss-Stream
	relies on the stability of the host path digest. The metric SHALL be		relies on the stability of the routers digest. The metric SHALL be
	invalid for times < T1 , T2, ..., Tm-1, Tm> if the following		invalid for times < T1 , T2, ..., Tm-1, Tm> if the following
	conditions occur:		conditions occur:
	o Ha or Hb disappears from the path due to some routing change.		o Ha or Hb disappears from the path due to some routing change.
	o The order of Ha and Hb changes in the path.		o The order of Ha and Hb changes in the path.
	o Lk.a or Lk.b is undefined.
			o Lk.a or Lk.b is undefined.
	o Lk.a has the value 1 (not observed) and Lk.b has the value 0		o Lk.a has the value 1 (not observed) and Lk.b has the value 0
	(observed);		(observed);
	o L has the value 0 (the packet was received by Dst) and Lk.ab has		o L has the value 0 (the packet was received by Dst) and Lk.ab has
	the value 1 (the packet was lost between Ha and Hb).		the value 1 (the packet was lost between Ha and Hb).
	6.3. A Definition of a Sample of ipdv of a Segment using the Previous		6.3. A Definition of a Sample of ipdv of a Segment using the Previous
	Packet Selection Function		Packet Selection Function
	This metric defines a sample of ipdv [RFC3393] over time between a		This metric defines a sample of ipdv [RFC3393] over time between a
	pair of hosts using the previous packet as the selection function.		pair of routers using the previous packet as the selection function.
	6.3.1. Metric Name		6.3.1. Metric Name
	Type-P-Segment-ipdv-prev-Stream		Type-P-Segment-ipdv-prev-Stream
	6.3.2. Metric Parameters		6.3.2. Metric Parameters
	o Src, the IP address of the sender.		o Src, the IP address of the sender.
	o Dst, the IP address of the receiver.		o Dst, the IP address of the receiver.
	o Type-P, the specification of the packet type.		o Type-P, the specification of the packet type.
	o k, an integer which orders the packets sent.		o k, an integer which orders the packets sent.
	o n, an integer which orders the hosts on the path.		o n, an integer which orders the routers on the path.
	o a and b, two integers where b > a.		o a and b, two integers where b > a.
	o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the hosts path digest.		o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers digest.
	o <T1, T2, ..., Tm-1, Tm>, a list of times.		o <T1, T2, ..., Tm-1, Tm>, a list of times.
	o <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a		o <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a
	Type-P-Spatial-One-way-Delay-Vector.		Type-P-Spatial-One-way-Delay-Vector.
	6.3.3. Metric Units		6.3.3. Metric Units
	The value of a Type-P-Segment-ipdv-prev-Stream is a pair of:		The value of a Type-P-Segment-ipdv-prev-Stream is a pair of:
	The list of <T1, T2, ..., Tm-1, Tm>;		The list of <T1, T2, ..., Tm-1, Tm>;
	A list of pairs of interval of times and delays;		A list of pairs of interval of times and delays;
	6.3.4. Definition		6.3.4. Definition
	Given two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,		Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,
	..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for		..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for
	the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :		the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :
	<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,		<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,
	<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,		<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,
	...		...
	<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.		<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.
	We define the Type-P-Segment-ipdv-prev-Stream as the sequence of		We define the Type-P-Segment-ipdv-prev-Stream as the sequence of
	packet time pairs and delay variations		packet time pairs and delay variations
	<(T1, T2 , dT2.ab - dT1.ab) ,...,		<(T1, T2 , dT2.ab - dT1.ab) ,...,
	(Tk-1, Tk, dTk.ab - dTk-1.ab), ...,		(Tk-1, Tk, dTk.ab - dTk-1.ab), ...,
	(Tm-1, Tm, dTm.ab - dTm-1.ab)>		(Tm-1, Tm, dTm.ab - dTm-1.ab)>
	For any pair, Tk, Tk-1 in k=1 through m, the difference dTk.ab - dTk-		For any pair, Tk, Tk-1 in k=1 through m, the difference dTk.ab - dTk-
	1.ab is undefined if:		1.ab is undefined if:
	o the delay dTk.a or the delay dTk-1.a is undefined, OR		o the delay dTk.a or the delay dTk-1.a is undefined, OR
	o the delay dTk.b or the delay dTk-1.b is undefined.		o the delay dTk.b or the delay dTk-1.b is undefined.
	6.3.5. Discussion		6.3.5. Discussion
	skipping to change at page 23, line 32		skipping to change at page 23, line 34
	control the ingress point of interest of the measure, Ha. The		control the ingress point of interest of the measure, Ha. The
	interval will certainly vary if there is delay variation between the		interval will certainly vary if there is delay variation between the
	Source and Ha. Therefore, the ingress inter-packet interval must be		Source and Ha. Therefore, the ingress inter-packet interval must be
	known at Ha in order to fully comprehend the delay variation between		known at Ha in order to fully comprehend the delay variation between
	Ha and Hb.		Ha and Hb.
	6.4. A Definition of a Sample of ipdv of a Segment using the Minimum		6.4. A Definition of a Sample of ipdv of a Segment using the Minimum
	Delay Selection Function		Delay Selection Function
	This metric defines a sample of ipdv [RFC3393] over time between a		This metric defines a sample of ipdv [RFC3393] over time between a
	pair of hosts on a path using the minimum delay as one of the		pair of routers on a path using the minimum delay as one of the
	selected packets in every pair.		selected packets in every pair.
	6.4.1. Metric Name		6.4.1. Metric Name
	Type-P-Segment-One-way-ipdv-min-Stream		Type-P-Segment-One-way-ipdv-min-Stream
	6.4.2. Metric Parameters		6.4.2. Metric Parameters
	o Src, the IP address of the sender.		o Src, the IP address of the sender.
	o Dst, the IP address of the receiver.		o Dst, the IP address of the receiver.
	o Type-P, the specification of the packet type.		o Type-P, the specification of the packet type.
	o k, an integer which orders the packets sent.		o k, an integer which orders the packets sent.
	o i, an integer which identifies a packet sent.		o i, an integer which identifies a packet sent.
	o n, an integer which orders the hosts on the path.		o n, an integer which orders the routers on the path.
	o a and b, two integers where b > a.		o a and b, two integers where b > a.
	o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the host path digest.
	o <T1, T2, ..., Tm-1, Tm>, a list of times.
			o <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers digest.
			o <T1, T2, ..., Tm-1, Tm>, a list of times.
	o <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a		o <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a
	Type-P-Spatial-One-way-Delay-Vector.		Type-P-Spatial-One-way-Delay-Vector.
	6.4.3. Metric Units		6.4.3. Metric Units
	The value of a Type-P-Segment-One-way-ipdv-min-Stream is a pair of:		The value of a Type-P-Segment-One-way-ipdv-min-Stream is a pair of:
	The list of <T1, T2, ..., Tm-1, Tm>;		The list of <T1, T2, ..., Tm-1, Tm>;
	A list of times.		A list of times.
	6.4.4. Definition		6.4.4. Definition
	Given two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,		Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,
	..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for		..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for
	the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :		the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :
	<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,		<T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,
	<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,		<T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,
	...		...
	<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.		<Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.
	We define the Type-P-Segment-One-way-ipdv-min-Stream as the sequence		We define the Type-P-Segment-One-way-ipdv-min-Stream as the sequence
	of times <dT1.ab - min(dTi.ab) ,..., dTk.ab - min(dTi.ab), ...,		of times <dT1.ab - min(dTi.ab) ,..., dTk.ab - min(dTi.ab), ...,
	dTm.ab - min(dTi.ab)> where:		dTm.ab - min(dTi.ab)> where:
	skipping to change at page 29, line 8		skipping to change at page 29, line 9
	former one only has statistics over the time dimension while the		former one only has statistics over the time dimension while the
	later one can have statistics over both time and space dimensions.		later one can have statistics over both time and space dimensions.
	This space dimension is introduced by the Matrix concept as		This space dimension is introduced by the Matrix concept as
	illustrated in Figure 4. For a Matrix M each row is a set of One-way		illustrated in Figure 4. For a Matrix M each row is a set of One-way
	singletons spreading over the time dimension and each column is		singletons spreading over the time dimension and each column is
	another set of One-way singletons spreading over the space dimension.		another set of One-way singletons spreading over the space dimension.
	Receivers		Receivers
	Space		Space
	^		^
	1 | / R1dT1 R1dT2 R1dT3 ... R3dTk \		1 | / R1dT1 R1dT2 R1dT3 ... R1dTk \
	| | |		| | |
	2 | | R2dT1 R2dT2 R2dT3 ... R3dTk |		2 | | R2dT1 R2dT2 R2dT3 ... R2dTk |
	| | |		| | |
	3 | | R3dT1 R3dT2 R3dT3 ... R3dTk |		3 | | R3dT1 R3dT2 R3dT3 ... R3dTk |
	. | | |		. | | |
	. | | |		. | | |
	. | | |		. | | |
	n | \ RndT1 RndT2 RndT3 ... RndTk /		n | \ RndT1 RndT2 RndT3 ... RndTk /
	+--------------------------------------------> time		+--------------------------------------------> time
	T0		T0
	Figure 4: Matrix M (n*m)		Figure 4: Matrix M (n*m)
	In Matrix M, each element is a one-way delay singleton. Each column		In Matrix M, each element is a one-way delay singleton. Each column
	is a delay vector contains the One-way delays of the same packet		is a delay vector. It contains the One-way delays of the same packet
	observed at M points of interest. It implies the geographical factor		observed at n points of interest. It implies the geographical factor
	of the performance within a group. Each row is a set of One-way		of the performance within a group. Each row is a set of One-way
	delays observed during a sampling interval at one of the points of		delays observed during a sampling interval at one of the points of
	interest. It presents the delay performance at a receiver over the		interest. It presents the delay performance at a receiver over the
	time dimension.		time dimension.
	Therefore, one can either calculate statistics by rows over the space		Therefore, one can either calculate statistics by rows over the space
	dimension or by columns over the time dimension. It's up to the		dimension or by columns over the time dimension. It's up to the
	operators or service provides which dimension they are interested in.		operators or service provides which dimension they are interested in.
	For example, a TV broadcast service provider might want to know the		For example, a TV broadcast service provider might want to know the
	statistical performance of each user in a long term run to make sure		statistical performance of each user in a long term run to make sure
	skipping to change at page 30, line 13		skipping to change at page 30, line 16
	Moreover, after knowing the statistics over the time dimension, one		Moreover, after knowing the statistics over the time dimension, one
	might want to know how these statistics are distributed over the		might want to know how these statistics are distributed over the
	space dimension. For instance, a TV broadcast service provider had		space dimension. For instance, a TV broadcast service provider had
	the performance Matrix M and calculated the One-way delay mean over		the performance Matrix M and calculated the One-way delay mean over
	the time dimension to obtain a delay Vector as {V1,V2,..., VN}. He		the time dimension to obtain a delay Vector as {V1,V2,..., VN}. He
	then calculated the mean of all the elements in the Vector to see		then calculated the mean of all the elements in the Vector to see
	what level of delay he has served to all N users. This new delay		what level of delay he has served to all N users. This new delay
	mean gives information on how good the service has been delivered to		mean gives information on how good the service has been delivered to
	a group of users during a sampling interval in terms of delay. It		a group of users during a sampling interval in terms of delay. It
	requires twice as much calculation to have this statistic over both		requires twice as much calculation to have this statistic over both
	time and space dimensions. This kind of statistics is referred to as		time and space dimensions. These kinds of statistics are referred to
	2-level statistics to distinguish them from 1-level statistics		as 2-level statistics to distinguish them from 1-level statistics
	calculated over either space or time dimension. It can be easily		calculated over either space or time dimension. It can be easily
	proven that no matter over which dimension a 2-level statistic is		proven that no matter over which dimension a 2-level statistic is
	calculated first, the results are the same. I.e. one can calculate		calculated first, the results are the same. I.e. one can calculate
	the 2-level delay mean using the Matrix M by having the 1-level delay		the 2-level delay mean using the Matrix M by having the 1-level delay
	mean over the time dimension first and then calculate the mean of the		mean over the time dimension first and then calculate the mean of the
	obtained vector to find out the 2-level delay mean. Or, he can do		obtained vector to find out the 2-level delay mean. Or, he can do
	the 1-level statistic calculation over the space dimension first and		the 1-level statistic calculation over the space dimension first and
	then have the 2-level delay mean. Both two results will be exactly		then have the 2-level delay mean. Both two results will be exactly
	the same. Therefore, when defining a 2-level statistic there is no		the same. Therefore, when defining a 2-level statistic there is no
	need to specify the order in which the calculation is executed.		need to specify the order in which the calculation is executed.
	skipping to change at page 30, line 37		skipping to change at page 30, line 40
	over either the space dimension or the time dimension or both. This		over either the space dimension or the time dimension or both. This
	memo treats the case where a stream of packets from the Source		memo treats the case where a stream of packets from the Source
	results in a sample at each of the Receivers in the Group, and these		results in a sample at each of the Receivers in the Group, and these
	samples are each summarized with the usual statistics employed in		samples are each summarized with the usual statistics employed in
	one-to-one communication. New statistic definitions are presented,		one-to-one communication. New statistic definitions are presented,
	which summarize the one-to-one statistics over all the Receivers in		which summarize the one-to-one statistics over all the Receivers in
	the Group.		the Group.
	8.1. Discussion on the Impact of packet loss on statistics		8.1. Discussion on the Impact of packet loss on statistics
	The packet loss does have effects on one-way metrics and their		Packet loss does have effects on one-way metrics and their
	statistics. For example, a lost packet can result in an infinite		statistics. For example, a lost packet can result in an infinite
	one-way delay. It is easy to handle the problem by simply ignoring		one-way delay. It is easy to handle the problem by simply ignoring
	the infinite value in the metrics and in the calculation of the		the infinite value in the metrics and in the calculation of the
	corresponding statistics. However, the packet loss has such a strong		corresponding statistics. However, the packet loss has such a strong
	impact on the statistics calculation for the one-to-group metrics		impact on the statistics calculation for the one-to-group metrics
	that it can not be solved by the same method used for one-way		that it can not be solved by the same method used for one-way
	metrics. This is due to the complexity of building a matrix, which		metrics. This is due to the complexity of building a matrix, which
	is needed for calculation of the statistics proposed in this memo.		is needed for calculation of the statistics proposed in this memo.
	The situation is that measurement results obtained by different end		The situation is that measurement results obtained by different end
	skipping to change at page 32, line 51		skipping to change at page 33, line 8
	Statistics are computed on the finite One-way delays of the matrix		Statistics are computed on the finite One-way delays of the matrix
	above.		above.
	All One-to-group delay statistics are expressed in seconds with		All One-to-group delay statistics are expressed in seconds with
	sufficient resolution to convey 3 significant digits.		sufficient resolution to convey 3 significant digits.
	8.3.1. Type-P-One-to-group-Receiver-n-Mean-Delay		8.3.1. Type-P-One-to-group-Receiver-n-Mean-Delay
	This section defines Type-P-One-to-group-Receiver-n-Mean-Delay the		This section defines Type-P-One-to-group-Receiver-n-Mean-Delay the
	Delay Mean at each Receiver N, also named RnDM.		Delay Mean at each Receiver N, also named RnMD.
	We obtain the value of Type-P-One-way-Delay singleton for all packets		We obtain the value of Type-P-One-way-Delay singleton for all packets
	sent during the test interval at each Receiver (Destination), as per		sent during the test interval at each Receiver (Destination), as per
	[RFC2679]. For each packet that arrives within Tmax of its sending		[RFC2679]. For each packet that arrives within Tmax of its sending
	time, TstampSrc, the one-way delay singleton (dT) will be the finite		time, TstampSrc, the one-way delay singleton (dT) will be the finite
	value TstampRecv[i] - TstampSrc[i] in units of seconds. Otherwise,		value TstampRecv[i] - TstampSrc[i] in units of seconds. Otherwise,
	the value of the singleton is Undefined.		the value of the singleton is Undefined.
	J[n]		J[n]
	---		---
	1 \		1 \
	RnMD = --- * > TstampRecv[i] - TstampSrc[i]		RnMD = --- * > TstampRecv[i] - TstampSrc[i]
	J[n] /		J[n] /
	---		---
	i = 1		i = 1
			Note: RnMD value is Undefined when J[n] = 0 for all n.
	Figure 6: Type-P-One-to-group-Receiver-N-Mean-Delay		Figure 6: Type-P-One-to-group-Receiver-N-Mean-Delay
	where all packets i= 1 through J[n] have finite singleton delays.		where all packets i= 1 through J[n] have finite singleton delays.
	8.3.2. Type-P-One-to-group-Mean-Delay		8.3.2. Type-P-One-to-group-Mean-Delay
	This section defines Type-P-One-to-group-Mean-Delay, the Mean One-way		This section defines Type-P-One-to-group-Mean-Delay, the Mean One-way
	delay calculated over the entire Group, also named GMD.		delay calculated over the entire Group, also named GMD.
	N		N
	---		---
	1 \		1 \
	GMD = - * > RnDM		GMD = - * > RnMD
	N /		N /
	---		---
	n = 1		n = 1
	Figure 7: Type-P-One-to-group-Mean-Delay		Figure 7: Type-P-One-to-group-Mean-Delay
	Note that the Group Mean Delay can also be calculated by summing the		Note that the Group Mean Delay can also be calculated by summing the
	Finite one-way Delay singletons in the Matrix, and dividing by the		Finite one-way Delay singletons in the Matrix, and dividing by the
	number of Finite One-way Delay singletons.		number of Finite One-way Delay singletons.
	8.3.3. Type-P-One-to-group-Range-Mean-Delay		8.3.3. Type-P-One-to-group-Range-Mean-Delay
	This section defines a metric for the range of mean delays over all N		This section defines a metric for the range of mean delays over all N
	receivers in the group (R1DM, R2DM,...RnDM).		receivers in the group (R1MD, R2MD...RnMD).
	Type-P-One-to-group-Range-Mean-Delay = GRMD = max(RnDM) - min(RnDM)		Type-P-One-to-group-Range-Mean-Delay = GRMD = max(RnMD) - min(RnMD)
	8.3.4. Type-P-One-to-group-Max-Mean-Delay		8.3.4. Type-P-One-to-group-Max-Mean-Delay
	This section defines a metric for the maximum of mean delays over all		This section defines a metric for the maximum of mean delays over all
	N receivers in the group (R1DM, R2DM,...RnDM).		N receivers in the group (R1MD, R2MD,...RnMD).
	Type-P-One-to-group-Max-Mean-Delay = GMMD = max(RnDM)		Type-P-One-to-group-Max-Mean-Delay = GMMD = max(RnMD)
	8.4. One-to-group Packet Loss Statistics		8.4. One-to-group Packet Loss Statistics
	This section defines the overall one-way loss statistics for a		This section defines the overall one-way loss statistics for a
	receiver and for an entire group as illustrated by the matrix below.		receiver and for an entire group as illustrated by the matrix below.
	Recv /----------- Sample ----------\ Stats Group Stat		Recv /----------- Sample ----------\ Stats Group Stat
	1 R1L1 R1L2 R1L3 ... R1Lk R1LR \		1 R1L1 R1L2 R1L3 ... R1Lk R1LR \
	|		|
	skipping to change at page 35, line 19		skipping to change at page 35, line 22
	---		---
	k = 1		k = 1
	Figure 9: Type-P-One-to-group-Receiver-n-Loss-Ratio		Figure 9: Type-P-One-to-group-Receiver-n-Loss-Ratio
	8.4.2. Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio		8.4.2. Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio
	Usually, the number of packets sent is used in the denominator of		Usually, the number of packets sent is used in the denominator of
	packet loss ratio metrics. For the comparative metrics defined here,		packet loss ratio metrics. For the comparative metrics defined here,
	the denominator is the maximum number of packets received at any		the denominator is the maximum number of packets received at any
	receiver for the sample and test interval of interest.		receiver for the sample and test interval of interest. The numerator
			is the sum of the losses at receiver n.
	The Comparative Loss Ratio, also named, RnCLR, is defined as		The Comparative Loss Ratio, also named, RnCLR, is defined as
	K		K
	---		---
	\		\
	> Ln(k)		> Ln(k)
	/		/
	---		---
	k=1		k=1
	RnCLR = -----------------------------		RnCLR = -----------------------------
	/ K \		/ K \
	| --- |		| --- |
	| \ |		| \ |
	K - Min | > Ln(k) |		K - Min | > Ln(k) |
	| / |		| / |
	| --- |		| --- |
	\ k=1 / N		\ k=1 / N
			Note: Ln is a set of one-way loss values at receiver n.
			There is one value for each of the K packets sent.
	Figure 10: Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio		Figure 10: Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio
	8.4.3. Type-P-One-to-group-Loss-Ratio		8.4.3. Type-P-One-to-group-Loss-Ratio
	Type-P-One-to-group-Loss-Ratio, the overall Group loss ratio, also		Type-P-One-to-group-Loss-Ratio, the overall Group loss ratio, also
	named GLR, is defined as		named GLR, is defined as
	K,N		K,N
	---		---
	1 \		1 \
	GLR = --- * > L(k,n)		GLR = --- * > Ln(k)
	K*N /		K*N /
	---		---
	k,n = 1		k,n = 1
	Figure 11: Type-P-One-to-group-Loss-Ratio		Figure 11: Type-P-One-to-group-Loss-Ratio
			Where the sum includes all of the Loss singletons, Ln(k), over the N
			receivers and K packets sent, in a ratio with the total packets over
			all receivers.
	8.4.4. Type-P-One-to-group-Range-Loss-Ratio		8.4.4. Type-P-One-to-group-Range-Loss-Ratio
	The One-to-group Loss Ratio Range is defined as:		The One-to-group Loss Ratio Range is defined as:
	Type-P-One-to-group-Range-Loss-Ratio = max(RnLR) - min(RnLR)		Type-P-One-to-group-Range-Loss-Ratio = max(RnLR) - min(RnLR)
	It is most effective to indicate the range by giving both the max and		It is most effective to indicate the range by giving both the max and
	minimum loss ratios for the Group, rather than only reporting the		minimum loss ratios for the Group, rather than only reporting the
	difference between them.		difference between them.
	skipping to change at page 38, line 37		skipping to change at page 38, line 46
	the sample session, and so on. Apparently, the centralized		the sample session, and so on. Apparently, the centralized
	calculation method can require much more bandwidth than the		calculation method can require much more bandwidth than the
	distributed calculation method when the sample size is big. This is		distributed calculation method when the sample size is big. This is
	especially true when the measurement has a very large number of the		especially true when the measurement has a very large number of the
	points of interest. It can lead to a scalability issue at the		points of interest. It can lead to a scalability issue at the
	reference point by overloading the network resources.		reference point by overloading the network resources.
	The distributed calculation method can save much more bandwidth and		The distributed calculation method can save much more bandwidth and
	mitigate issues arising from scalability at the reference point side.		mitigate issues arising from scalability at the reference point side.
	However, it may result in a lost of information. As all measured		However, it may result in a loss of information. As not all measured
	singletons are not available for building up the group matrix, the		singletons are available for building up the group matrix, the real
	real performance over time can be hidden from the result. For		performance over time can be hidden from the result. For example,
	example, the loss pattern can be missed by simply accepting the loss		the loss pattern can be missed by simply accepting the loss ratio.
	ratio. This tradeoff between bandwidth consumption and information		This tradeoff between bandwidth consumption and information
	acquisition has to be taken into account when designing the		acquisition has to be taken into account when designing the
	measurement approach.		measurement approach.
	One possible solution could be to transit the statistic parameters to		One possible solution could be to transmit the statistic parameters
	the reference point first to obtain the general information of the		to the reference point first to obtain the general information of the
	group performance. If detailed results are required, the reference		group performance. If detailed results are required, the reference
	point should send the requests to the points of interest, which could		point should send the requests to the points of interest, which could
	be particular ones or the whole group. This procedure can happen in		be particular ones or the whole group. This procedure can happen in
	the off peak time and can be well scheduled to avoid delivery of too		the off peak time and can be well scheduled to avoid delivery of too
	many points of interest at the same time. Compression techniques can		many points of interest at the same time. Compression techniques can
	also be used to minimize the bandwidth required by the transmission.		also be used to minimize the bandwidth required by the transmission.
	This could be a measurement protocol to report the measurement		This could be a measurement protocol to report the measurement
	results. However, this is out of the scope of this memo.		results. However, this is out of the scope of this memo.
	9.2. Measurement		9.2. Measurement
	To prevent any bias in the result, the configuration of a one-to-many		To prevent any bias in the result, the configuration of a one-to-many
	measure must take in consideration that intrically more packets will		measure must take in consideration that more packets will to be
	to be routed than sent (copies of a packet sent are expected to		routed than sent (copies of a packet sent are expected to arrive at
	arrive at many destination points) and selects a test packets rate		many destination points) and selects a test packets rate that will
	that will not impact the network performance.		not impact the network performance.
	9.3. Effect of Time and Space Aggregation Order on Stats		9.3. Effect of Time and Space Aggregation Order on Stats
	This section presents the impact of the aggregation order on the		This section presents the impact of the aggregation order on the
	scalability of the reporting and of the computation. It makes the		scalability of the reporting and of the computation. It makes the
	hypothesis that receivers are not co-located and that results are		hypothesis that receivers are not co-located and that results are
	gathered in a point of reference for further usages.		gathered in a point of reference for further usages.
	Multimetrics samples are represented in a matrix as illustrated below		Multimetrics samples are represented in a matrix as illustrated below
	Point of		Point of
	interest		interest
	1 R1S1 R1S1 R1S1 ... R1Sk \		1 R1S1 R1S1 R1S1 ... R1Sk \
	|		|
	2 R2S1 R2S2 R2S3 ... R2Sk |		2 R2S1 R2S2 R2S3 ... R2Sk |
	|		|
	3 R3S1 R3S2 R3S3 ... R3Sk > sample over space		3 R3S1 R3S2 R3S3 ... R3Sk > sample over space
	. |		. |
	. |		. |
	. |		. |
	skipping to change at page 40, line 50		skipping to change at page 41, line 30
	Two methods are available to compute group statistics:		Two methods are available to compute group statistics:
	o Method1: Figure 5 and Figure 8 illustrate the method chosen: the		o Method1: Figure 5 and Figure 8 illustrate the method chosen: the
	one-to-one statistic is computed per interval of time before the		one-to-one statistic is computed per interval of time before the
	computation of the mean over the group of receivers;		computation of the mean over the group of receivers;
	o Method2: Figure 13 presents the second one, metric is computed		o Method2: Figure 13 presents the second one, metric is computed
	over space and then over time.		over space and then over time.
	10. Manageability Considerations		10. Manageability Considerations
	Usually IPPM WG documents defines each metric reporting within its		This section defines the reporting of all the metrics introduced in
	definition. This document defines the reporting of all the metrics		the document.
	introduced in a single section to provide consistent information, to
	avoid repetitions and to conform to IESG recommendation of gathering
	manageability considerations in a dedicated section.
	Information models of spatial metrics and of one-to-group metrics are		Information models of spatial metrics and of one-to-group metrics are
	similar excepted that points of interests of spatial vectors must be		similar excepted that points of interests of spatial vectors MUST be
	ordered.		ordered.
	The complexity of the reporting relies on the number of points of		The complexity of the reporting relies on the number of points of
	interests.		interests.
	10.1. Reporting spatial metric		10.1. Reporting spatial metric
	The reporting of spatial metrics shares a lot of aspects with		The reporting of spatial metrics shares a lot of aspects with
	RFC2679-80. New ones are common to all the definitions and are		RFC2679-80. New ones are common to all the definitions and are
	mostly related to the reporting of the path and of methodology		mostly related to the reporting of the path and of methodology
	parameters that may bias raw results analysis. This section presents		parameters that may bias raw results analysis. This section presents
	these specific parameters and then lists exhaustively the parameters		these specific parameters and then lists exhaustively the parameters
	that shall be reported.		that SHOULD be reported.
	10.1.1. Path		10.1.1. Path
	End-to-end metrics can't determine the path of the measure despite		End-to-end metrics can't determine the path of the measure despite
	IPPM RFCs recommend it to be reported (See Section 3.8.4 of		IPPM RFCs recommend it to be reported (See Section 3.8.4 of
	[RFC2679]). Spatial metrics vectors provide this path. The report		[RFC2679]). Spatial metrics vectors provide this path. The report
	of a spatial vector must include the points of interests involved:		of a spatial vector MUST include the points of interests involved:
	the sub set of the hosts of the path participating to the		the sub set of the routers of the path participating to the
	instantaneous measure.		instantaneous measure.
	10.1.2. Host order		10.1.2. Host order
	A spatial vector must order the points of interest according to their		A spatial vector MUST order the points of interest according to their
	order in the path. It is highly suggested to use the TTL in IPv4,		order in the path. The ordering MAY be based on information from the
	the Hop Limit in IPv6 or the corresponding information in MPLS.		TTL in IPv4, the Hop Limit in IPv6 or the corresponding information
			in MPLS.
	The report of a spatial vector must include the ordered list of the		The report of a spatial vector MUST include the ordered list of the
	hosts involved in the instantaneous measure.		hosts involved in the instantaneous measure.
	10.1.3. Timestamping bias		10.1.3. Timestamping bias
	The location of the point of interest inside a node influences the		The location of the point of interest inside a node influences the
	timestamping skew and accuracy. As an example, consider that some		timestamping skew and accuracy. As an example, consider that some
	internal machinery delays the timestamping up to 3 milliseconds then		internal machinery delays the timestamping up to 3 milliseconds then
	the minimal uncertainty reported be 3 ms if the internal delay is		the minimal uncertainty reported be 3 ms if the internal delay is
	unknown at the time of the timestamping.		unknown at the time of the timestamping.
	The report of a spatial vector must include the uncertainty of the		The report of a spatial vector MUST include the uncertainty of the
	timestamping compared to wire time.		timestamping compared to wire time.
	10.1.4. Reporting spatial One-way Delay		10.1.4. Reporting spatial One-way Delay
	The reporting includes information to report for one-way-delay as the		The reporting includes information to report for one-way-delay as the
	Section 3.6 of [RFC2679]. The same apply for packet loss and ipdv.		Section 3.6 of [RFC2679]. The same apply for packet loss and ipdv.
	10.2. Reporting One-to-group metric		10.2. Reporting One-to-group metric
	All reporting rules described in [RFC2679] and [RFC2680] apply to the		All reporting rules described in [RFC2679] and [RFC2680] apply to the
	corresponding One-to-group metrics. Following are specific		corresponding One-to-group metrics. Following are specific
	parameters that should be reported.		parameters that SHOULD be reported.
	10.2.1. Path		10.2.1. Path
	As suggested by the [RFC2679] and [RFC2680], the path traversed by		As suggested by the [RFC2679] and [RFC2680], the path traversed by
	the packet SHOULD be reported, if possible. For One-to-group		the packet SHOULD be reported, if possible. For One-to-group
	metrics, the path tree between the source and the destinations or the		metrics, the path tree between the source and the destinations or the
	set of paths between the source and each destination SHOULD be		set of paths between the source and each destination SHOULD be
	reported.		reported.
	Path tree might not be as valuable as individual paths because an		Path tree might not be as valuable as individual paths because an
	incomplete path might be difficult to identify in the path tree. For		incomplete path might be difficult to identify in the path tree. For
	example, how many points of interest are reached by a packet		example, how many points of interest are reached by a packet
	travelling along an incomplete path?		travelling along an incomplete path?
	10.2.2. Group size		10.2.2. Group size
	The group size should be reported as one of the critical management		The group size SHOULD be reported as one of the critical management
	parameters. One-to-group metrics, unlike spatial metrics, don't		parameters. One-to-group metrics, unlike spatial metrics, don't
	require the ordering of the points of interests because group members		require the ordering of the points of interests because group members
	receive the packets in parallel.		receive the packets in parallel.
	10.2.3. Timestamping bias		10.2.3. Timestamping bias
	It is the same as described in section 10.1.3.		It is the same as described in section 10.1.3.
	10.2.4. Reporting One-to-group One-way Delay		10.2.4. Reporting One-to-group One-way Delay
	It is the same as described in section 10.1.4.		It is the same as described in section 10.1.4.
	10.2.5. Measurement method		10.2.5. Measurement method
	As explained in section 9, the measurement method will have impact on		As explained in section 9, the measurement method will have impact on
	the analysis of the measurement result. Therefore, it should be		the analysis of the measurement result. Therefore, it SHOULD be
	reported.		reported.
	10.3. Metric identification		10.3. Metric identification
	IANA assigns each metric defined by the IPPM WG with a unique		IANA assigns each metric defined by the IPPM WG with a unique
	identifier as per [RFC4148] in the IANA-IPPM-METRICS-REGISTRY-MIB.		identifier as per [RFC4148] in the IANA-IPPM-METRICS-REGISTRY-MIB.
	10.4. Information model		10.4. Information model
	This section presents the elements of information and the usage of		This section presents the elements of information and the usage of
	skipping to change at page 43, line 32		skipping to change at page 44, line 9
	Uncertainties".		Uncertainties".
	Following are the elements of information taken from end-to-end		Following are the elements of information taken from end-to-end
	metrics definitions referred in this memo and from spatial and		metrics definitions referred in this memo and from spatial and
	multicast metrics it defines:		multicast metrics it defines:
	o Packet_type, The Type-P of test packets (Type-P);		o Packet_type, The Type-P of test packets (Type-P);
	o Packet_length, a packet length in bits (L);		o Packet_length, a packet length in bits (L);
	o Src_host, the IP address of the sender;		o Src_host, the IP address of the sender;
	o Dst_host, the IP address of the receiver;		o Dst_host, the IP address of the receiver;
	o Hosts_serie: <H1, H2,..., Hn>, a list of points of interest;		o Hosts_serie: <H1, H2,..., Hn>, a list of points of interest
			participating to the instantaneous measure. They are routers in
			the case of spatial metrics or receivers in the case of one-to-
			group metrics;
	o Loss_threshold: The threshold of infinite delay;		o Loss_threshold: The threshold of infinite delay;
	o Systematic_error: constant delay between wire time and		o Systematic_error: constant delay between wire time and
	timestamping;		timestamping;
	o Calibration_error: maximal uncertainty;		o Calibration_error: maximal uncertainty;
	o Src_time, the sending time for a measured packet;		o Src_time, the sending time for a measured packet;
	o Dst_time, the receiving time for a measured packet;		o Dst_time, the receiving time for a measured packet;
	o Result_status : an indicator of usability of a result 'Resource		o Result_status : an indicator of usability of a result 'Resource
	exhaustion' 'infinite', 'lost';		exhaustion' 'infinite', 'lost';
	o Delays_serie: <dT1,..., dTn> a list of delays;		o Delays_serie: <dT1,..., dTn> a list of delays;
	o Losses_serie: <B1, B2, ..., Bi, ..., Bn>, a list of Boolean values		o Losses_serie: <B1, B2, ..., Bi, ..., Bn>, a list of Boolean values
	(spatial) or a set of Boolean values (one-to-group);		(spatial) or a set of Boolean values (one-to-group);
	o Result_status_serie: a list of results status;		o Result_status_serie: a list of results status;
	o dT: a delay;		o dT: a delay;
	o Singleton_number: a number of singletons;		o Singleton_number: a number of singletons;
	o Observation_duration: An observation duration;		o Observation_duration: An observation duration;
	o metric_identifier.		o metric_identifier.
	Following is the information of each vector that should be available		Following is the information of each vector that SHOULD be available
	to compute samples:		to compute samples:
	o Packet_type;		o Packet_type;
	o Packet_length;		o Packet_length;
	o Src_host, the sender of the packet;		o Src_host, the sender of the packet;
	o Dst_host, the receiver of the packet, apply only for spatial		o Dst_host, the receiver of the packet, apply only for spatial
	vectors;		vectors;
	o Hosts_serie: not ordered for one-to-group;		o Hosts_serie: not ordered for one-to-group;
	o Src_time, the sending time for the measured packet;		o Src_time, the sending time for the measured packet;
	o dT, the end-to-end one-way delay for the measured packet, apply		o dT, the end-to-end one-way delay for the measured packet, apply
	only for spatial vectors;		only for spatial vectors;
	o Delays_serie: apply only for delays and ipdv vector, not ordered		o Delays_serie: apply only for delays and ipdv vector, not ordered
	for one-to-group;		for one-to-group;
	o Losses_serie: apply only for packets loss vector, not ordered for		o Losses_serie: apply only for packets loss vector, not ordered for
	one-to-group;		one-to-group;
	o Result_status_serie;		o Result_status_serie;
	o Observation_duration: the difference between the time of the last		o Observation_duration: the difference between the time of the last
	singleton and the time of the first singleton.		singleton and the time of the first singleton.
	o Following is the context information (measure, points of		o Following is the context information (measure, points of
	interests) that should be available to compute samples :		interests) that SHOULD be available to compute samples :
	* Loss threshold;		* Loss threshold;
	* Systematic error: constant delay between wire time and		* Systematic error: constant delay between wire time and
	timestamping;		timestamping;
	* Calibration error: maximal uncertainty;		* Calibration error: maximal uncertainty;
	A spatial or a one-to-group sample is a collection of singletons		A spatial or a one-to-group sample is a collection of singletons
	giving the performance from the sender to a single point of interest.		giving the performance from the sender to a single point of interest.
	Following is the information that should be available for each sample		Following is the information that SHOULD be available for each sample
	to compute statistics:		to compute statistics:
	o Packet_type;		o Packet_type;
	o Packet_length;		o Packet_length;
	o Src_host, the sender of the packet;		o Src_host, the sender of the packet;
	o Dst_host, the receiver of the packet;		o Dst_host, the receiver of the packet;
	o Start_time, the sending time of the first packet;		o Start_time, the sending time of the first packet;
	o Delays_serie: apply only for delays and ipdv samples;		o Delays_serie: apply only for delays and ipdv samples;
	o Losses_serie: apply only for packets loss samples;		o Losses_serie: apply only for packets loss samples;
	o Result_status_serie;		o Result_status_serie;
	o Observation_duration: the difference between the time of the last		o Observation_duration: the difference between the time of the last
	singleton of the last sample and the time of the first singleton		singleton of the last sample and the time of the first singleton
	of the first sample.		of the first sample.
	o Following is the context information (measure, points of		o Following is the context information (measure, points of
	interests) that should be available to compute statistics :		interests) that SHOULD be available to compute statistics :
	* Loss threshold;		* Loss threshold;
	* Systematic error: constant delay between wire time and		* Systematic error: constant delay between wire time and
	timestamping;		timestamping;
	* Calibration error: maximal uncertainty;		* Calibration error: maximal uncertainty;
	Following is the information of each statistic that should be		Following is the information of each statistic that SHOULD be
	reported:		reported:
	o Result;		o Result;
	o Start_time;		o Start_time;
	o Duration;		o Duration;
	o Result_status;		o Result_status;
	o Singleton_number, the number of singletons the statistic is		o Singleton_number, the number of singletons the statistic is
	computed on;		computed on;
	11. Security Considerations		11. Security Considerations
	Spatial and one-to-group metrics are defined on the top of end-to-end		Spatial and one-to-group metrics are defined on the top of end-to-end
	metrics. Security considerations discussed in One-way delay metrics		metrics. Security considerations discussed in One-way delay metrics
	definitions of [RFC2679] , in packet loss metrics definitions of		definitions of [RFC2679] , in packet loss metrics definitions of
	[RFC2680] and in IPDV metrics definitions of[RFC3393] and [RFC3432]		[RFC2680] and in IPDV metrics definitions of[RFC3393] and [RFC3432]
	apply to metrics defined in this memo.		apply to metrics defined in this memo.
	11.1. Spatial metrics		Someone may spoof the identity of a Point of interest identity and
			intentionally send corrupt results in order to remotely orient the
			traffic engineering decisions.
	Malicious generation of packets with spoofing addresses may corrupt		A point of interest could intentionally corrupt its results in order
	the results without any possibility to detect the spoofing.		to remotely orient the traffic engineering decisions.
			11.1. Spatial metrics
	Malicious generation of packets which match systematically the hash		Malicious generation of packets which match systematically the hash
	function used to detect the packets may lead to a DoS attack toward		function used to detect the packets may lead to a DoS attack toward
	the point of reference.		the point of reference.
			Spatial measurement results carry the performance of individual
			segments of the path and the identity of nodes. An attacker may
			infer from this information the points of weakness of a network (e.g.
			congested node) which would require the least amount of additional
			attacking traffic to exploit. Therefore, monitoring information
			should be carried in a way which prevents unintended recipients from
			inspecting the measurement reports. A straight forward solution is
			to restrict access to the reports using encrypted sessions or secured
			networks.
	11.2. One-to-group metrics		11.2. One-to-group metrics
	Reporting of measurement results from a huge number of probes may		Reporting of measurement results from a huge number of probes may
	overload reference point resources (network, network interfaces,		overload reference point resources (network, network interfaces,
	computation capacities ...).		computation capacities ...).
	The configuration of a measurement must take in consideration that		The configuration of a measurement must take in consideration that
	implicitly more packets will be routed than sent and selects a test		implicitly more packets will be routed than sent and selects a test
	packets rate accordingly. Collecting statistics from a huge number		packets rate accordingly. Collecting statistics from a huge number
	of probes may overload any combination of the network where the		of probes may overload any combination of the network where the
	measurement controller is attached to, measurement controller network		measurement controller is attached to, measurement controller network
	interfaces and measurement controller computation capacities.		interfaces and measurement controller computation capacities.
	One-to-group metrics measurement should consider using source		One-to-group metrics measurement should consider using source
	authentication protocols, standardized in the MSEC group, to avoid		authentication protocols, standardized in the MSEC group, to avoid
	fraud packet in the sampling interval. The test packet rate could be		fraud packet in the sampling interval. The test packet rate could be
	negotiated before any measurement session to avoid deny of service		negotiated before any measurement session to avoid deny of service
	attacks.		attacks.
			A point of interest could intentionally degrade its results in order
			to remotely increase the quality of the network on the branches of
			the multicast tree it is connected to.
	12. Acknowledgments		12. Acknowledgments
	Lei would like to acknowledge Prof. Zhili Sun from CCSR, University		Lei would like to acknowledge Prof. Zhili Sun from CCSR, University
	of Surrey, for his instruction and helpful comments on this work.		of Surrey, for his instruction and helpful comments on this work.
	13. IANA Considerations		13. IANA Considerations
	Metrics defined in this memo Metrics defined in this memo are		Metrics defined in this memo are designed to be registered in the
	designed to be registered in the IANA IPPM METRICS REGISTRY as		IANA IPPM METRICS REGISTRY as described in initial version of the
	described in initial version of the registry [RFC4148] :		registry [RFC4148] :
	IANA is asked to register the following metrics in the IANA-IPPM-		IANA is asked to register the following metrics in the IANA-IPPM-
	METRICS-REGISTRY-MIB :		METRICS-REGISTRY-MIB :
	ietfSpatialOneWayDelayVector OBJECT-IDENTITY		ietfSpatialOneWayDelayVector OBJECT-IDENTITY
	STATUS current		STATUS current
	DESCRIPTION		DESCRIPTION
	"Type-P-Spatial-One-way-Delay-Vector"		"Type-P-Spatial-One-way-Delay-Vector"
	REFERENCE		REFERENCE
	"Reference "RFCyyyy, section 5.1."		"Reference "RFCyyyy, section 5.1."
	skipping to change at page 51, line 9		skipping to change at page 52, line 9
	Metric for IP Performance Metrics (IPPM)", RFC 3393,		Metric for IP Performance Metrics (IPPM)", RFC 3393,
	November 2002.		November 2002.
	[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics		[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
	Registry", BCP 108, RFC 4148, August 2005.		Registry", BCP 108, RFC 4148, August 2005.
	14.2. Informative References		14.2. Informative References
	[I-D.ietf-ippm-spatial-composition]		[I-D.ietf-ippm-spatial-composition]
	Morton, A. and E. Stephan, "Spatial Composition of		Morton, A. and E. Stephan, "Spatial Composition of
	Metrics", draft-ietf-ippm-spatial-composition-08 (work in		Metrics", draft-ietf-ippm-spatial-composition-09 (work in
	progress), March 2009.		progress), June 2009.
	[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,		[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
	"Framework for IP Performance Metrics", RFC 2330,		"Framework for IP Performance Metrics", RFC 2330,
	May 1998.		May 1998.
	[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network		[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
	performance measurement with periodic streams", RFC 3432,		performance measurement with periodic streams", RFC 3432,
	November 2002.		November 2002.
	Authors' Addresses		Authors' Addresses
End of changes. 116 change blocks.
	163 lines changed or deleted		195 lines changed or added
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